Steffen Rebennack

Robert Fabian Lindermann, Paul-Niklas Ken Kandora, Simon Caspar Zeller et al.

We study shortest-path routing in large weighted, undirected graphs, where expanding search frontiers raise time and memory costs for exact solvers. We propose \emph{SPHERE}, a query-aware partitioning heuristic that adaptively splits the problem by identifying \emph{source-target} ($s$--$t$) overlaps of hop-distance spheres. Selecting an anchor node $a$ within this overlap partitions the task into independent induced subgraphs for $s\to a$ and $a\to t$, each restricted to its own induced subgraph. If resulting subgraphs remain large, the procedure recurses on that specific subgraph. We provide a formal guarantee that by using the partition cut within the shared overlap, the resulting subpaths preserve feasibility, thereby avoiding the need for boundary repair. Furthermore, \emph{SPHERE} acts as a solver-agnostic framework that naturally exposes parallelism across subproblems. On million-scale road networks, \emph{SPHERE} achieves faster runtimes and smaller optimality gaps than contemporary state-of-the-art partitioning and community-based routing pipelines. Crucially, it also substantially mitigates heavy-tail runtime outliers suffered by standard exact methods, yielding highly stable and predictable execution times across varying queries.

Paul-Niklas Ken Kandora, Simon Caspar Zeller, Aaron Jeremias Elsing et al.

Reformulating nonlinear optimization problems is largely manual and expertise-intensive, yet it remains essential for solving such problems with linear optimization solvers or applying special-purpose algorithms. We introduce \textit{LinearizeLLM}, an agent-based framework that solves this task by leveraging Large Language Models (LLMs). The framework assigns each nonlinear pattern to a \textit{reformulation agent} that is explicitly instructed to derive an exact linear reformulation for its nonlinearity pattern, for instance, absolute-value terms or bilinear products of decision variables. The agents then coordinate to assemble a solver-ready linear model equivalent to the original problem. To benchmark the approach, we create a dataset of 20 real-world nonlinear optimization problems derived from the established ComplexOR dataset of linear optimization problems. We evaluate our approach with several LLMs. Our results indicate that specialized LLM agents can automate linearization tasks, opening a path toward fully conversational modeling pipelines for nonlinear optimization.